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### Colloquia

Colloquia for the Department of Mathematics and Statistics are normally
held in **University Hall 4010 on Fridays at 4:00pm**.
Any departures from this are indicated below.

Light refreshments are served after the colloquia in 2040 University Hall.

Driving directions, parking information, and maps are available on the university website.

# 2015-2016 Colloquia

What follows is a list of speakers, talk titles and abstracts for the current academic year. Abstracts for the talks are also posted in the hallways around the departmental offices.

## Fall Semester

- November 20, 2015
Britni Balint (Women in Mathematics - National Security Agency)

*Secret Lives of Mathematicians*Abstract: Mathematics can be more than just a subject in school, it can be a career. The government is the number one single employer of mathematicians in the country. Many of those mathematicians end up at the National Security Agency, where they find careers in research, information assurance, and cryptanalysis. This talk will be an introduction to the roles of mathematicians at NSA, as well as basics of cryptography.

- November 13, 2015
Jeffrey Morton (University of Toledo)

*Introduction to Topological Quantum Field Theory in 2 Dimensions*Abstract: This talk gives an introductory view of topological quantum field theory (TQFT) from a category-theoretic point of view. I will explain what a TQFT is and introduce the necessary ideas from category theory, leading to an explanation of how a TQFT can be described as a kind of monoidal functor. Then I will describe how, for 2-dimensional spacetimes, this means that a TQFT is equivalent to a certain kind of bialgebra called a Frobenius algebra.

- October 16, 2015
Logan Hoehn (Nipissing University)

*A Complete Classification of Homogeneous Plane Continua*Abstract: A space X is homogeneous if for every pair of points in X, there is a homeomorphism of X onto itself taking one point to the other. Kuratowski and Knaster asked in 1920 whether the circle is the only homogeneous compact connected space (continuum) in the plane. Explorations of this problem fueled a significant amount of research in continuum theory, and among other things, led to the discovery of two new homogeneous continua in the plane: the pseudo-arc and the circle of pseudo-arcs. I will describe our recent result which shows that there are no more undiscovered homogeneous compact connected spaces in the plane. Our result actually can be used to show that we have determined all compact homogeneous spaces in the plane.

This is joint work with Lex G. Oversteegen, University of Alabama at Birmingham.

- October 9, 2015
Morley Davidson (Kent State University)

*Calculating the maximum number of moves needed to solve Rubik's Cube*Abstract: The problem of determining the Cube's diameter, ie. maximum number of moves required to solve an arbitrary scrambling, goes back to the puzzle's origins circa 1980. In the last few years the problem was finished off for the two most popular ways of counting moves, the "half-turn" and "quarter-turn" metrics, with the help of supercomputers at Google and the Ohio Supercomputer Center, respectively. In this talk we discuss the mathematical and algorithmic tricks that made these computations possible and affordable with present-day machinery.

- October 2, 2015 (UH 4480)
Yichuan Zhao (Georgia State University)

*Smoothed Jackknife Empirical Likelihood Inference for the Difference of ROC Curves*Abstract: For the comparison of two diagnostic markers at a flexible specificity, people apply the difference of two correlated receiver operating characteristic (ROC) curves to identify the diagnostic test with stronger discriminant ability. In this paper, we employ jackknife empirical likelihood (JEL) method to construct confidence intervals for the difference of two correlated continuous-scale ROC curves. Using the jackknife pseudo-sample, we can avoid estimating several nuisance variables which have to be estimated in existing methods. We prove that the smoothed jackknife empirical log likelihood ratio is asymptotically chi-squared distribution. Furthermore, the simulation studies in terms of coverage probability and average length of confidence intervals show the good performance in small samples with a moderate computational cost. A real data set is used to illustrated our method.

- October 2, 2015
Leonard Scott (The University of Virginia)

*Finite and algebraic groups, some history and a recent application*Abstract: The interrelationship of finite and algebraic group theory, together with modern computer calculations (let me mention Frank Luebeck, and my own student, Tim Sprowl), led to the demise in 2012 of a 1961 conjecture of G. E. Wall related to finite group permutation actions. Stated in abstract group theory terms, the conjecture asserted that the number of maximal subgroups of a given finite group G was less than the number of elements of G. It was known to be true for all solvable finite groups and almost all finite simple groups, yet there are infinitely many counterexamples. The part played by algebraic group theory brought together several quite substantial developments in the subject, part and parcel of a historical march and a bigger picture, involving not only group actions and subgroups, but also representation theory and cohomology. The role of a conjecture of Lusztig on algebraic group representations — true for very large prime field characteristics — stands out, as does work of Cline-Parshall-Scott-van der Kallen relating cohomology of these representations to the finite group case.

- Shoemaker Lecture III September 25, 2015, Friday, 10:00-11:00am in UH 4010
Amie Wilkinson (University of Chicago)

*Robust mechanisms for chaos, II: Stable ergodicity and partial hyperbolicity*Abstract: Kolmogorov introduced in the 1950's a robust mechanism for non-ergodicity, which is now known as the KAM phenomenon (named for Kologorov, Arnol'd and Moser). A current, pressing problem in smooth dynamics is to understand the interplay between KAM and Hopf phenomena in specific classes of dynamical systems. I will describe a class of dynamical systems, called the partially hyperbolic systems, in which the two phenomena can in some sense be combined. I'll also explain recent results that give strong evidence for the truth of a modified ergodic hypothesis in this setting, known as the Pugh-Shub stable ergodicity conjecture.

- Shoemaker Lecture II September 24, 2015, Thursday, 4:00-5:00pm in UH 4010
Amie Wilkinson (University of Chicago)

*Robust mechanisms for chaos, I: Geometry and the birth of stable ergodicity*Abstract: The first general, robust mechanism for ergodicity was developed by E. Hopf in the 1930's in the context of Riemannian geometry. Loosely put, Hopf showed that for a negatively curved, compact surface, the “typical” infinite geodesic fills the manifold in a very uniform way, a property called equidistribution. I will discuss Hopf's basic idea in both topological and measure-theoretic settings and how it has developed into a widely applicable mechanism for chaotic behavior in smooth dynamics.

- Shoemaker Lecture I September 23, 2015, Wednesday, 4:00-5:00pm in GH 5300
Amie Wilkinson (University of Chicago)

*The Ergodic Hypothesis and Beyond - "The General Case"*Abstract: The celebrated Ergodic Theorems of George Birkhoff and von Neumann in the 1930's gave rise to a mathematical formulation of Boltzmann's Ergodic Hypothesis in thermodynamics. This reformulated hypothesis has been described by a variety of authors as the conjecture that ergodicity -- a form of randomness of orbit distributions -- should be "the general case" in conservative dynamics. I will discuss remarkable discoveries in the intervening century that show why such a hypothesis must be false in its most restrictive formulation but still survives in some contexts. In the end, I will begin to tackle the question, "When is ergodicity and other chaotic behavior the general case?"